Math 389: Advanced Analysis First Lecture

Size: px

Start display at page:

Download "Math 389: Advanced Analysis First Lecture"

Leona Heath
5 years ago
Views:

1 Math 389: Advanced Analysis First Lecture Steven J Miller Williams College sjm1@williams.edu Bronfman B34 Williams College, September 5, 2014

2 Introduction and Objectives

3 Introduction / Objectives Objectives Obviously learn advanced analysis. Emphasize techniques / asking the right questions. Find out if grad school (in math) is what you want. Help you get into grad school (or a job,...). Writing textbook, broader impact activities (MathSciNet, refereeing, math riddles).

4 Types of Problems Benford s Law. The Circle Method: Goldbach, Twin Primes, Sophie Germain Primes,... L-Functions and Random Matrix Theory. Poissonian Behavior....

5 5 Introduction Mechanics Useful Links Course Mechanics

6 Grading / Administrative Homework: 20%, Midterm 20%, Final / Research Project 20%, Class Presentation: 20%, Broader Impact Projects: 20% Pre-reqs: real analysis (complex analysis, probability, programming a plus). Office hours / feedback TBD and when I m in my office (schedule online). Feedback ephsmath@gmail.com, password first 8 Fibonacci numbers ( ).

7 7 Introduction Mechanics Useful Links Other Webpage: numerous handouts, additional comments each day (mix of review and optional advanced material). Opportunity to help write a book. PREPARE FOR CLASS! Must do readings before each class.

8 Erdős Numbers and Generalizations My Erdős number is 2, Erdős-Bacon number is unclear, but...

9 Erdős Numbers and Generalizations My Erdős number is 2, Erdős-Bacon number is unclear, but...

10 Other: Advice from Jeff Miller Party less than the person next to you.

11 Other: Advice from Jeff Miller Party less than the person next to you. Take advantage of office hours / mentoring.

12 Other: Advice from Jeff Miller Party less than the person next to you. Take advantage of office hours / mentoring. Learn to manage your time: no one else wants to.

13 Other: Advice from Jeff Miller Party less than the person next to you. Take advantage of office hours / mentoring. Learn to manage your time: no one else wants to. Happy to do practice interviews, adjust deadlines...

14 Useful links

15 LaTeX and Mathematica Tutorials and Templates Has templates for using LaTeX for papers, talks, posters, and a Mathematica tutorial. Also videos on each.

16 GRE GRE links: CALCULUS: 50%: Material learned in the usual sequence of elementary calculus courses differential and integral calculus of one and of several variables: includes calculus-based applications and connections with coordinate geometry, trigonometry, differential equations and other branches of mathematics. ALGEBRA: 25%: Elementary algebra: basic algebraic techniques and manipulations acquired in high school and used throughout mathematics Linear algebra: matrix algebra, systems of linear equations, vector spaces, linear transformations, characteristic polynomials and eigenvalues and eigenvectors Abstract algebra and number theory: elementary topics from group theory, theory of rings and modules, field theory and number theory. ADDITIONAL TOPICS: 25%: Introductory real analysis: sequences and series of numbers and functions, continuity, differentiability and integrability, and elementary topology of R and R n, Discrete mathematics: logic, set theory, combinatorics, graph theory and algorithms. Other topics: general topology, geometry, complex variables, probability and statistics, and numerical analysis.

Department of Mathematics The Ohio State University

Department of Mathematics The Ohio State University 2002-2003 Mathematics Courses Course Number Course Title 50 Pre-College Mathematics I 75 Pre-College Mathematics II 76 Reentry Precollege Math 103 Enrichment